How to create convincing rain with a particle system
I assume you know how basic particle systems work.
If not i recommend watching a tutorial on basic particle systems (like this one).

Just spawn the particles like you would do normally. 

Then add collision to your surface (the creature in the gif from your op) and set the Particle Dampening.



As you can see on the image, some particles are bouncing off, some sliding down the surface.
Hope it helps.